Seismic risk and possible maximum loss (PML) analysis of reinforced concrete structures - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 740

Moreover, the use of the multi-event approach facilitates the develop-
ment of other related seismic risk curves and quantities. Two seismic risk
indices/quantities, NEL and PML, can be derived for each scenario as
follows:

c

max

∫

()

NEL = c f ⋅ c j d c [27.4]

j C

0

PML j

∫

()

09 . = fcj c d [27.5]

C

0

NEL j is the expected seismic loss for the j th scenario, whereas the PML j is
defi ned as the 0.9-fractile value for the j th scenario (i.e. PML j will be
exceeded with 10% chance given the occurrence of the scenario). By repeat-
ing the evaluations of NEL and PML for all major scenarios, seismic risk
curves based on NEL/PML can be developed. An illustration of the NEL
and PML seismic risk curves is also given in Fig. 27.2; the PML curve is
plotted on the right-hand side of the NEL curve, indicating greater seismic
loss level. The use of these two risk curves may be benefi cial as they capture
different aspects of the seismic loss distribution (i.e. average versus right
upper tail), especially for risk-based quantitative seismic risk management
of buildings and infrastructure. (Note: the risk characteristics for rare events
are of particular concern for risk undertakers, such as insurers and reinsur-
ers.) In Japan, the return period level of 475 years (i.e. 90% non-exceedance
probability in 50 years) is a popular probability level that is often consid-
ered for seismic risk assessment (see Fig. 27.2).

27.3 Case studies of seismic risk analysis for

reinforced concrete structures

In this section, four case studies for quantitative seismic risks analysis for
reinforced concrete structures in Japan are discussed. The aim of this section
is to introduce practical applications of the above-mentioned analytical
procedures and to demonstrate how such assessments can facilitate
informed decision-making related to earthquake risk mitigation.

27.3.1 Railway viaduct

A railway system is an important infrastructure for urban intercity traffi c,
and provides daily mass transportation in the metropolitan area. In the
metropolitan city of Tokyo, there are numerous railway viaducts due to
limited space for transportation and complex confi gurations of major high-
ways. Typical railway viaducts in Japan are reinforced concrete frame struc-
tures. Two case studies that consider old and current versions for Design